Question

# Check that the ratio ke2 /G memp is dimensionless. Look up a Table of Physical Constants and determine the value of this ratio. What does the ratio signify?

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#### The given ratio is ke2GmcmpWhere,G= Gravitational constantIts unit is Nm2kg−2.me and mp= Masses of electron and proton.Their unit is kg.e= Electric charge.Its unit is C.k=A constant =14π∈0∈0= Permittivity of free spaceIts unit is Nm2C−2. Unit of the given ratio ke2Gmcmp=[Nm2C2][C−2][Nm2kg−2][kg][kg] =M0L0T0Hence, the given ratio is dimensionless.e=1.6×10−19CG=6.67×10−11Nm2kg−2me=9.1×106−31kgmp=1.66×10−27kgke2Gmcmp=9×109×(1.6×10−19)26.67×10−11×9.1×10−3×1.67×10−22≈2.3×1039This is the ratio of electric force to the gravitational force between a proton and an electron, keeping distance between them constant.

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